Swansea and Stoke were also believed to have been tracking his progress but Cardiff have beaten them to the punch.
The clubs have agreed a fee and Odemwingie is understood to be happy with the personal terms being offered by the newly-promoted Welsh side.
The 32-year-old has also been granted a work permit by the Home Office which he would require to change clubs and the deal is expected to be completed ahead of the 11pm transfer deadline.
Odemwingie almost left The Hawthorns in January and turned up outside Loftus Road as he looked to push through a move to QPR.
That transfer never materialised and instead he has found himself pushed towards the fringes of Steve Clarke's squad.
Despite that, Odemwingie still registered 10 goals in 25 appearances for the Baggies last season and Cardiff boss Malky Mackay will be hopeful he can reproduce his best form for the south Wales club.